She shouldn't be carrying on an affair WHILE she is still living in your house, right?
You could just simply tell her that it's time for her to look for somewhere else to live, that you are not ok sharing your home with her while she's involved with another person.
Period.
Now Johnny, this is NOT a chance for you to grandstand.
This is NOT a chance for you to condemn, make a point, show her how wonderful you are.
This is you laying down the law. It moves you STRONGLE closer to a divorce. But we recognize that divorce is not necessarily the end, right?
If you're going to do this and become a basket case while you try to pull it off, you better leave it alone.
If you're going to do this and be an unmitigated ass hole while doing it, you should probably put it off.
But if you simply can't take it anymore, nothing wrong with moving forward.
Blessings,
Bill
"Don't tell me the sky is the limit when there are footprints on the moon."